Let's denote the roots of the quadratic equation as x1 and x2.
First, we know that the sum of the roots is given by the formula:
x1 + x2 = -b/a
where a and b are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In our equation, since the sum of the roots is 5/2, we have:
x1 + x2 = 5/2
Next, we know that the product of the roots is given by the formula:
x1 * x2 = c/a
In our equation, since the product of the roots is 4, we have:
x1 * x2 = 4
Now, let's find the equations based on the given information.
From the equation x1 + x2 = 5/2, we can rewrite it as:
x1 = 5/2 - x2
Plugging this into our product of the roots equation, we have:
(5/2 - x2) * x2 = 4
Simplifying, we get:
5x2 - 2x2^2 = 8
Rearranging the equation and simplifying further, we have:
2x2^2 - 5x2 + 8 = 0
Therefore, the quadratic equation is 2x^2 - 5x + 8 = 0, which corresponds to option B.
12. The sum of the roots of a quadratic
equation is 5
2
and the product of its roots is
4. The quadratic equation is____
A. 2x2 + 5x + 8 = 0
B. 2x2 — 5x + 8 = 0
C. 2x2 — 8x + 5 = 0
D. 2x2 + 8x — 5 = 0
1 answer